Cremona's table of elliptic curves

1616 = 2⁴ · 101

Field	Data	Notes
Atkin-Lehner	2+ 101+	Signs for the Atkin-Lehner involutions
Class	1616b	Isogeny class
Conductor	1616	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	224	Modular degree for the optimal curve
Δ	25856 = 28 · 101	Discriminant
Eigenvalues	2+ -2  3 -2  2 -3  3 -5	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-129,523]	[a1,a2,a3,a4,a6]
Generators	[6:1:1]	Generators of the group modulo torsion
j	934577152/101	j-invariant
L	2.3460716484933	L(r)(E,1)/r!
Ω	3.6141833615563	Real period
R	0.64912911543122	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	808b1 6464n1 14544h1 40400c1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1616b1

a2	a3	a5	a7	a11	a13	a17	a19	a23	a29	a31	a37	a41	a43	a47	a53	a59	a61	a67	a71	a73	a79	a83	a89	a97
+	-2	3	-2	2	-3	3	-5	-3	-8	3	-2	-4	8	-5	-2	-10	12	2	1	4	-13	0	-14	-14

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Quadratic twists for elliptic curve 1616b1

-4	8	-3	5	-7
808b1	6464n1	14544h1	40400c1	79184n1

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Data from Elliptic Curve Data by J. E. Cremona.
Design inspired by The Modular Forms Explorer by William Stein.

Part of Computational Number Theory
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